The purpose of this study is to prove the Collatz conjecture using a theorem proving system. First, the division sequence is defined as an alignment of the number of times division by 2 is performed in the Collatz ope...The purpose of this study is to prove the Collatz conjecture using a theorem proving system. First, the division sequence is defined as an alignment of the number of times division by 2 is performed in the Collatz operation. Then, the star conversion is defined, which is a mapping from a specific division sequence to a division sequence. Here it is important to map to some division sequence, not which division sequence. The important point is that the finite length of the division sequence does not change before and after the star conversion. In theorem proving system, we considered two parallel methods: main-proof is a claim to a computer proposition that has the same meaning as the Collatz conjecture. Theorem proving support system “Idris” was used. Moreover, we sub-proved that the 12 “extended star conversion” are closed to the “Collatz operation”. Egison’s computer algebra system is used for proof. The results of the two methods achieved the goal of proving the Collatz conjecture using a theorem proving system.展开更多
The phase change of lacustrine gravity flow deposition is fast and complex. In its reservoir division and correlation, the isochronous problem is very important. Taking the oil formation I of Es3 in Wuhaozhuang oilfie...The phase change of lacustrine gravity flow deposition is fast and complex. In its reservoir division and correlation, the isochronous problem is very important. Taking the oil formation I of Es3 in Wuhaozhuang oilfield as an example, through the analysis of stratigraphic drilling and logging data in the study area, according to the genetic types of different levels of base level cycle interfaces and the characteristics of high-resolution sequence stratigraphy, this paper subdivides the lacustrine gravity flow oil layer of lower Es3 in Wuhaozhuang Oilfield, divides it into four short-term base level cycle sequences, and establishes the high-resolution isochronous stratigraphic framework of this interval. It is found that the mid-term, short-term and ultra short-term base level cycles correspond to the oil formation, sand layer group and single layer in the oil layer correlation unit of the oilfield respectively. Based on this, the oil layer correlation unit of the interval is divided, and the sublayer correlation model is established according to the identification characteristics of the short-term base level cycle.展开更多
To achieve virtual full-duplex(VFD)communication using half-duplex radios,the rapid on-off-division(RODD)technique has been proposed in recent years.The time-hopping(TH)sequence is critical to controlling self-interfe...To achieve virtual full-duplex(VFD)communication using half-duplex radios,the rapid on-off-division(RODD)technique has been proposed in recent years.The time-hopping(TH)sequence is critical to controlling self-interference introduced in the paradigm.By constructing the collision model with a symbol level time scale,the periodic collision correlation function properties are introduced as the performance metric for the TH sequence in the RODD system.To achieve the best VFD performance,an optimization-based method for TH sequence design is proposed.In addition,the conventional TH frame structure design for RODD system is improved.Numerical simulations are presented to demonstrate that the proposed approach can significantly increase system performance.Results indicate that the TH sequence design is very effective for the RODD system.展开更多
The concept of the binary sequence pair is generalized from a single binary sequence. Binary sequence pairs are applied in many fields of radar, sonar or communication systems, in which signals with optimal periodic c...The concept of the binary sequence pair is generalized from a single binary sequence. Binary sequence pairs are applied in many fields of radar, sonar or communication systems, in which signals with optimal periodic correlation are required. Several types of almost perfect binary sequence pairs of length T = 2q are constructed, where q is an odd number. These almost perfect binary sequence pairs are based on binary ideal sequence or binary ideal two-level correlation sequence pairs by using Chinese remainder theorem. For these almost perfect binary sequence pairs with good balanced property, their corresponding divisible difference set pairs(DDSPs) are also derived.展开更多
In this paper, a new partial transmit sequence（PTS）scheme with low computational complexity is proposed for the problems of high computational complexity in the conventional PTS method. By analyzing the relationship...In this paper, a new partial transmit sequence（PTS）scheme with low computational complexity is proposed for the problems of high computational complexity in the conventional PTS method. By analyzing the relationship of candidate sequences in the PTS method under the interleaved partition method, it has been discovered that some candidate sequences generated by phase factor sequences have the same peak average power ratio（PAPR）. Hence, phase factor sequences can be optimized to reduce their searching times. Then, the computational process of generating candidate sequences can be simplified by improving the utilization of data and minimizing the calculations of complex multiplication. The performance analysis shows that, compared with the conventional PTS scheme, the proposed approach significantly decreases the computational complexity and has no loss of PAPR performance.展开更多
This paper deals with optimal training design and placement over multiple orthogonal frequency division multiplexing(OFDM) symbols for the least squares(LS) channel estimation in multiple-input multipleoutput(MIMO) OF...This paper deals with optimal training design and placement over multiple orthogonal frequency division multiplexing(OFDM) symbols for the least squares(LS) channel estimation in multiple-input multipleoutput(MIMO) OFDM systems.First,the optimal pilot sequences over multiple OFDM symbols are derived by co-cyclic Jacket matrices based on the minimum mean square error(MSE) of the LS channel estimation.Then,an enhanced channel estimation method using sliding window is proposed to improve further the performance for the optimal pilot sequences in fast-varying channels.Simulation results show that the enhancedmethod can efficiently improve the performances for the optimal pilot sequences over two and four OFDM symbols,especially in fast-varying channels.展开更多
Partial transmit sequence (PTS) is a promising technique for peak-to-average power ratio (PAPR) re-duction in orthogonal frequency division multiplexing (OFDM). While in optimal PTS, an exhaustive search for all combi...Partial transmit sequence (PTS) is a promising technique for peak-to-average power ratio (PAPR) re-duction in orthogonal frequency division multiplexing (OFDM). While in optimal PTS, an exhaustive search for all combinations of phase factor sequences is required, this results in huge computation. In this paper, by introducing the orthogonal design, a phase factor sequences algorithm is proposed. The algorithm uses orthogonal table to gen-erate phase factor sequences, and the regular PAPR computation result is then followed by the parameter estima-tion. The simulation result shows that the proposed algorithm reduces the computation notably and obtains a good PAPR performance approaching the optimal PTS.展开更多
In an Approximately Synchronized Code Division Multiple Access (AS-CDMA) commu-nication system,a family with large number of Zero Correlation Zone (ZCZ) sequences is desired,which can satisfy the rapid increase of use...In an Approximately Synchronized Code Division Multiple Access (AS-CDMA) commu-nication system,a family with large number of Zero Correlation Zone (ZCZ) sequences is desired,which can satisfy the rapid increase of users. This paper presents a method to generate a (2L ,2M ,Zc' z )-ZCZsequence family from an original (L ,M ,Z cz)-ZCZsequence family,where Z c' z =Zcz if Z czis even and Z c' z = Zcz 1if Z czis odd. This method can also recursively act on a ZCZ sequence family to construct a series of ZCZ sequence families with large sequence number and zero correlation zone length identical to or one less than that of original ZCZ sequences.展开更多
Many nitrogen-containing aromatic compounds （NACs）, such as nitrobenzene （NB）, 4-nitrophenol （4-NP）, aniline （AN）, and 2,4-dinitrophenol （2,4-DNP）, are environmentally hazardous, and their removal from conta...Many nitrogen-containing aromatic compounds （NACs）, such as nitrobenzene （NB）, 4-nitrophenol （4-NP）, aniline （AN）, and 2,4-dinitrophenol （2,4-DNP）, are environmentally hazardous, and their removal from contaminated water is one of the main challenges facing wastewater treatment plants. In this study, synthetic wastewater containing NB, 4-NP, 2,4-DNP, and AN at concentrations ranging from 50 to 180 mg/L was fed into a sequencing batch reactor （SBR）. Analyses of the SBR system indicated that it simultaneously removed more than 99% of the NACs at loading rates of 0.36 kg NB/（m^3·d）, 0.3 kg 4-NP/（m^3·d）, 0.25 kg AN/（m^3·d）, and 0.1 kg 2,4-DNP/（m^3·d）. Bacterial groups of Bacteriodetes, Candidate division TM7, α-Proteobacteria, and β-Proteobacteria were dominant in the clone libraries of 16S rRNA genes retrieved from the microbial communities in the SBR system. ＂Cycle tests＂ designed to alter feeding and aeration parameters of the SBR system demonstrated that the resident microbial biome of the SBR system responded rapidly to changing conditions. Consumption of O2 was concomitant with the apparent mineralization of NACs. Aromatic ring-cleaving dioxygenase activities suggested that （1） AN and NB were degraded via catechol 2,3-dioxygenase; （2） 4-NP was degraded via 1,2,4-benzentriol 1,2-dioxygenase; and （3） 2,4-DNP was degraded via an unresolved pathway.展开更多
文摘The purpose of this study is to prove the Collatz conjecture using a theorem proving system. First, the division sequence is defined as an alignment of the number of times division by 2 is performed in the Collatz operation. Then, the star conversion is defined, which is a mapping from a specific division sequence to a division sequence. Here it is important to map to some division sequence, not which division sequence. The important point is that the finite length of the division sequence does not change before and after the star conversion. In theorem proving system, we considered two parallel methods: main-proof is a claim to a computer proposition that has the same meaning as the Collatz conjecture. Theorem proving support system “Idris” was used. Moreover, we sub-proved that the 12 “extended star conversion” are closed to the “Collatz operation”. Egison’s computer algebra system is used for proof. The results of the two methods achieved the goal of proving the Collatz conjecture using a theorem proving system.
文摘The phase change of lacustrine gravity flow deposition is fast and complex. In its reservoir division and correlation, the isochronous problem is very important. Taking the oil formation I of Es3 in Wuhaozhuang oilfield as an example, through the analysis of stratigraphic drilling and logging data in the study area, according to the genetic types of different levels of base level cycle interfaces and the characteristics of high-resolution sequence stratigraphy, this paper subdivides the lacustrine gravity flow oil layer of lower Es3 in Wuhaozhuang Oilfield, divides it into four short-term base level cycle sequences, and establishes the high-resolution isochronous stratigraphic framework of this interval. It is found that the mid-term, short-term and ultra short-term base level cycles correspond to the oil formation, sand layer group and single layer in the oil layer correlation unit of the oilfield respectively. Based on this, the oil layer correlation unit of the interval is divided, and the sublayer correlation model is established according to the identification characteristics of the short-term base level cycle.
基金Supported by the National Key Basic Research Program of China(973 Program)(613314)
文摘To achieve virtual full-duplex(VFD)communication using half-duplex radios,the rapid on-off-division(RODD)technique has been proposed in recent years.The time-hopping(TH)sequence is critical to controlling self-interference introduced in the paradigm.By constructing the collision model with a symbol level time scale,the periodic collision correlation function properties are introduced as the performance metric for the TH sequence in the RODD system.To achieve the best VFD performance,an optimization-based method for TH sequence design is proposed.In addition,the conventional TH frame structure design for RODD system is improved.Numerical simulations are presented to demonstrate that the proposed approach can significantly increase system performance.Results indicate that the TH sequence design is very effective for the RODD system.
基金supported by the National Natural Science Foundation of China(6160140161501395+6 种基金6160139961671402)Natural Science Foundation of Hebei Province(F2015203150F2016203293F2016203312)Natural Science Research Programs of Hebei Educational Committee(QN2016120)the Independent Research Programs for Young Teachers of Yanshan University(15LGB013)
文摘The concept of the binary sequence pair is generalized from a single binary sequence. Binary sequence pairs are applied in many fields of radar, sonar or communication systems, in which signals with optimal periodic correlation are required. Several types of almost perfect binary sequence pairs of length T = 2q are constructed, where q is an odd number. These almost perfect binary sequence pairs are based on binary ideal sequence or binary ideal two-level correlation sequence pairs by using Chinese remainder theorem. For these almost perfect binary sequence pairs with good balanced property, their corresponding divisible difference set pairs(DDSPs) are also derived.
基金supported by the National Natural Science Foundation of China(6167309361370152)the Science and Technology Project of Shenyang(F16-205-1-01)
文摘In this paper, a new partial transmit sequence（PTS）scheme with low computational complexity is proposed for the problems of high computational complexity in the conventional PTS method. By analyzing the relationship of candidate sequences in the PTS method under the interleaved partition method, it has been discovered that some candidate sequences generated by phase factor sequences have the same peak average power ratio（PAPR）. Hence, phase factor sequences can be optimized to reduce their searching times. Then, the computational process of generating candidate sequences can be simplified by improving the utilization of data and minimizing the calculations of complex multiplication. The performance analysis shows that, compared with the conventional PTS scheme, the proposed approach significantly decreases the computational complexity and has no loss of PAPR performance.
基金the National Natural Science Foundation of China (Nos. 60332030 and 60625103)the Science and Technology Commission of Shanghai Municipality (STCSM) (No. 05DZ22102)the National High Technology Research and Development Program(863) of China (No. 2007AA01Z237)
文摘This paper deals with optimal training design and placement over multiple orthogonal frequency division multiplexing(OFDM) symbols for the least squares(LS) channel estimation in multiple-input multipleoutput(MIMO) OFDM systems.First,the optimal pilot sequences over multiple OFDM symbols are derived by co-cyclic Jacket matrices based on the minimum mean square error(MSE) of the LS channel estimation.Then,an enhanced channel estimation method using sliding window is proposed to improve further the performance for the optimal pilot sequences in fast-varying channels.Simulation results show that the enhancedmethod can efficiently improve the performances for the optimal pilot sequences over two and four OFDM symbols,especially in fast-varying channels.
基金Supported by Tianjin Natural Science Foundation (No. 043600611)Key Scientific and Technological Training Program of Tianjin (No. 043102911).
文摘Partial transmit sequence (PTS) is a promising technique for peak-to-average power ratio (PAPR) re-duction in orthogonal frequency division multiplexing (OFDM). While in optimal PTS, an exhaustive search for all combinations of phase factor sequences is required, this results in huge computation. In this paper, by introducing the orthogonal design, a phase factor sequences algorithm is proposed. The algorithm uses orthogonal table to gen-erate phase factor sequences, and the regular PAPR computation result is then followed by the parameter estima-tion. The simulation result shows that the proposed algorithm reduces the computation notably and obtains a good PAPR performance approaching the optimal PTS.
基金the National Natural Science Foundation of China (No.60673081)the National "863" Project (No.2006AA01Z417).
文摘In an Approximately Synchronized Code Division Multiple Access (AS-CDMA) commu-nication system,a family with large number of Zero Correlation Zone (ZCZ) sequences is desired,which can satisfy the rapid increase of users. This paper presents a method to generate a (2L ,2M ,Zc' z )-ZCZsequence family from an original (L ,M ,Z cz)-ZCZsequence family,where Z c' z =Zcz if Z czis even and Z c' z = Zcz 1if Z czis odd. This method can also recursively act on a ZCZ sequence family to construct a series of ZCZ sequence families with large sequence number and zero correlation zone length identical to or one less than that of original ZCZ sequences.
基金Project supported by the Pilot Project of Knowledge Innovation Program of Chinese Academy of Sciences (No. KZCX2-YW-G-009)the National Natural Science Foundation of China (No. 20577067, 30230010).
文摘Many nitrogen-containing aromatic compounds （NACs）, such as nitrobenzene （NB）, 4-nitrophenol （4-NP）, aniline （AN）, and 2,4-dinitrophenol （2,4-DNP）, are environmentally hazardous, and their removal from contaminated water is one of the main challenges facing wastewater treatment plants. In this study, synthetic wastewater containing NB, 4-NP, 2,4-DNP, and AN at concentrations ranging from 50 to 180 mg/L was fed into a sequencing batch reactor （SBR）. Analyses of the SBR system indicated that it simultaneously removed more than 99% of the NACs at loading rates of 0.36 kg NB/（m^3·d）, 0.3 kg 4-NP/（m^3·d）, 0.25 kg AN/（m^3·d）, and 0.1 kg 2,4-DNP/（m^3·d）. Bacterial groups of Bacteriodetes, Candidate division TM7, α-Proteobacteria, and β-Proteobacteria were dominant in the clone libraries of 16S rRNA genes retrieved from the microbial communities in the SBR system. ＂Cycle tests＂ designed to alter feeding and aeration parameters of the SBR system demonstrated that the resident microbial biome of the SBR system responded rapidly to changing conditions. Consumption of O2 was concomitant with the apparent mineralization of NACs. Aromatic ring-cleaving dioxygenase activities suggested that （1） AN and NB were degraded via catechol 2,3-dioxygenase; （2） 4-NP was degraded via 1,2,4-benzentriol 1,2-dioxygenase; and （3） 2,4-DNP was degraded via an unresolved pathway.
